Question

IF THE COEFFICIENT OF x IN THE EXPANISION OF (1+ax)^8 (1+3x)^4 - (1-x)^3 (1+2x)^4 IS ZERO THEN FIND THE VALUE 0F A

Answer 1

( 1 + ax)⁸ = ⁸C₀ + ⁸C₁ ax......

Coefficient of x = ⁸C₁ a = 8a

( 1 + 3x)⁴ = ⁴C₀ + ⁴C₁ 3x

Coefficient of x = ⁴C₁ a = 4*3 = 12

( 1 - x) ³ = ³C₀ - ³C₁ x

Coefficient of x = - ³C₁ a = - 3

( 1 +2x)⁴ = ⁴C₀ + ⁴C₁ 2x

Coefficient of x = ⁴C₁ 2 = 4 *2 = 8

=> 8a × 12 - ( - 3) × 8 = 0

=> 96a + 24 = 0

=> 96a = - 24

=> a = - 24 / 96

=> a = - 2 / 8

=> a = - 1 /4.